Set Theory and Logic

    

Terms Constructed by the "Diagonal Method" Are Unclosed Terms

Authors: Jincheng Zhang

Nature of a proposition constructed by diagonal method of proof is a paradox, so it is an unclosed term and an extra-field proposition. There are two kinds of infinities, standard infinity and non-standard infinity, and we will explore the diagonal problem in each of the two kinds of infinities below.We conclude that: (1) In standard infinity, Cantor's diagonal number can metamorphose into real number and the contradiction vanishes. (2) In nonstandard infinity, Cantor's diagonal numbers become hyperreal number . Essentially both are unclosed terms of the calculation.Therefore, Cantor's diagonal method proves that "the real numbers are not countable" is wrong.

Comments: 9 Pages.

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[v1] 2023-03-30 02:54:04

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